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Title: SEM-EBSD based Realistic Modeling and Crystallographic Homogenization FE Analyses of LDH Formability Tests

Abstract

Homogenization algorithm is introduced to the elastic/crystalline viscoplastic finite element (FE) procedure to develop multi-scale analysis code to predict the formability of sheet metal in macro scale, and simultaneously the crystal texture and hardening evolutions in micro scale. The isotropic and kinematical hardening lows are employed in the crystalline plasticity constitutive equation. For the multi-scale structure, two scales are considered. One is a microscopic polycrystal structure and the other a macroscopic elastic plastic continuum. We measure crystal morphologies by using the scanning electron microscope (SEM) with electron back scattered diffraction (EBSD), and define a three dimensional representative volume element (RVE) of micro ploycrystal structure, which satisfy the periodicity condition of crystal orientation distribution. Since nonlinear multi-scale FE analysis requires large computation time, development of parallel computing technique is needed. To realize the parallel analysis on PC cluster system, the dynamic explicit FE formulations are employed. Applying the domain partitioning technique to FE mesh of macro continuum, homogenized stresses based on micro crystal structures are computed in parallel without solving simultaneous linear equation. The parallel FEM code is applied to simulate the limit dome height (LDH) test problem and hemispherical cup deep drawing problem of aluminum alloy AL6022, mild steel DQSK,more » high strength steel HSLA, and dual phase steel DP600 sheet metals. The localized distribution of thickness strain and the texture evolution are obtained.« less

Authors:
;  [1]; ;  [2];  [3];  [4]
  1. Faculty of Engineering, Osaka Institute of Technology, 5-16-1 Omiya, Asahi-ku, Osaka 535-8585 (Japan)
  2. Osaka Sangyo University, 3-1-1 Nakagaito, Daito Osaka 574-8530 (Japan)
  3. Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555 (Japan)
  4. Furukawa Electric Co. Ltd., 2-4-3 Okano, Nishi-ku, Yokohama 220-0073 (Japan)
Publication Date:
OSTI Identifier:
21057350
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 908; Journal Issue: 1; Conference: NUMIFORM '07: 9. international conference on numerical methods in industrial forming processes, Porto (Portugal), 17-21 Jun 2007; Other Information: DOI: 10.1063/1.2740799; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; ALUMINIUM ALLOYS; BACKSCATTERING; CARBON STEELS; COMPUTERIZED SIMULATION; CRYSTAL STRUCTURE; DRAWING; ELECTRON DIFFRACTION; FINITE ELEMENT METHOD; HARDENING; METALS; MORPHOLOGY; NONLINEAR PROBLEMS; PLASTICITY; POLYCRYSTALS; SCANNING ELECTRON MICROSCOPY; SHEETS; STRAINS; STRESSES; TEXTURE

Citation Formats

Kuramae, Hiroyuki, Nakamachi, Eiji, Ngoc Tam, Nguyen, Nakamura, Yasunori, Sakamoto, Hidetoshi, and Morimoto, Hideo. SEM-EBSD based Realistic Modeling and Crystallographic Homogenization FE Analyses of LDH Formability Tests. United States: N. p., 2007. Web. doi:10.1063/1.2740799.
Kuramae, Hiroyuki, Nakamachi, Eiji, Ngoc Tam, Nguyen, Nakamura, Yasunori, Sakamoto, Hidetoshi, & Morimoto, Hideo. SEM-EBSD based Realistic Modeling and Crystallographic Homogenization FE Analyses of LDH Formability Tests. United States. doi:10.1063/1.2740799.
Kuramae, Hiroyuki, Nakamachi, Eiji, Ngoc Tam, Nguyen, Nakamura, Yasunori, Sakamoto, Hidetoshi, and Morimoto, Hideo. Thu . "SEM-EBSD based Realistic Modeling and Crystallographic Homogenization FE Analyses of LDH Formability Tests". United States. doi:10.1063/1.2740799.
@article{osti_21057350,
title = {SEM-EBSD based Realistic Modeling and Crystallographic Homogenization FE Analyses of LDH Formability Tests},
author = {Kuramae, Hiroyuki and Nakamachi, Eiji and Ngoc Tam, Nguyen and Nakamura, Yasunori and Sakamoto, Hidetoshi and Morimoto, Hideo},
abstractNote = {Homogenization algorithm is introduced to the elastic/crystalline viscoplastic finite element (FE) procedure to develop multi-scale analysis code to predict the formability of sheet metal in macro scale, and simultaneously the crystal texture and hardening evolutions in micro scale. The isotropic and kinematical hardening lows are employed in the crystalline plasticity constitutive equation. For the multi-scale structure, two scales are considered. One is a microscopic polycrystal structure and the other a macroscopic elastic plastic continuum. We measure crystal morphologies by using the scanning electron microscope (SEM) with electron back scattered diffraction (EBSD), and define a three dimensional representative volume element (RVE) of micro ploycrystal structure, which satisfy the periodicity condition of crystal orientation distribution. Since nonlinear multi-scale FE analysis requires large computation time, development of parallel computing technique is needed. To realize the parallel analysis on PC cluster system, the dynamic explicit FE formulations are employed. Applying the domain partitioning technique to FE mesh of macro continuum, homogenized stresses based on micro crystal structures are computed in parallel without solving simultaneous linear equation. The parallel FEM code is applied to simulate the limit dome height (LDH) test problem and hemispherical cup deep drawing problem of aluminum alloy AL6022, mild steel DQSK, high strength steel HSLA, and dual phase steel DP600 sheet metals. The localized distribution of thickness strain and the texture evolution are obtained.},
doi = {10.1063/1.2740799},
journal = {AIP Conference Proceedings},
number = 1,
volume = 908,
place = {United States},
year = {Thu May 17 00:00:00 EDT 2007},
month = {Thu May 17 00:00:00 EDT 2007}
}
  • A crystallographic homogenization procedure is introduced to the conventional static-explicit and dynamic-explicit finite element formulation to develop a multi scale - double scale - analysis code to predict the plastic strain induced texture evolution, yield loci and formability of sheet metal. The double-scale structure consists of a crystal aggregation - micro-structure - and a macroscopic elastic plastic continuum. At first, we measure crystal morphologies by using SEM-EBSD apparatus, and define a unit cell of micro structure, which satisfy the periodicity condition in the real scale of polycrystal. Next, this crystallographic homogenization FE code is applied to 3N pure-iron and 'Benchmark'more » aluminum A6022 polycrystal sheets. It reveals that the initial crystal orientation distribution - the texture - affects very much to a plastic strain induced texture and anisotropic hardening evolutions and sheet deformation. Since, the multi-scale finite element analysis requires a large computation time, a parallel computing technique by using PC cluster is developed for a quick calculation. In this parallelization scheme, a dynamic workload balancing technique is introduced for quick and efficient calculations.« less
  • Crystallographic analysis of plate martensite in an Fe-28.5 at.% Ni alloy was studied by electron backscattering diffraction (EBSD) in a scanning electron microscope equipped with a field emission gun (FE-SEM). It was shown that sound orientation mapping was possible even for the martensite having a high density of lattice defects and the FE-SEM/EBSD could be a strong tool for crystallographic/microstructural analysis of martensite in steels. It was confirmed that the martensite in this alloy held the Nishiyama-Wassermann (N-W) orientation relationship. Variant analysis of every martensite crystal was successfully done from orientation mapping data. It was clarified that a certain rulemore » of variant selection operated within local areas. The procedures of crystallographic analysis of N-W martensite were explained in detail.« less
  • Recently, the multi scale analysis technology, by using the crystallographic homogenization based dynamic explicit finite element code, has been developed to assess macro continuum sheet material properties and further study the deformation and straining in the actual sheet forming. This homogenization finite element code employs the two scale hierarchical structure, which consists of a polycrystal microstructure and a macro continuum. In this study, for the reality, we focus to discuss 'How to define a proper microstructure for the two scale finite element analysis, by employing the real measurement base polycrystal aggregation, which has been obtained by SEM-EBSD' observations. For scalingmore » up from the micro polycrystal structure to the macro continuum, we define a unit cell by looking at the periodicity of crystal orientation, which is one of morphological factors to feature the polycrystal structure, which is named as 'texture'. Through a statistical study of these measured polycrystal morphologies, finally we found a realistic polycrystal unit cell of the microstructure, which can be adopted for our multi scale finite element analyses.« less
  • Since the multi-scale finite element analysis (FEA) requires large computation time, development of the parallel computing technique for the multi-scale analysis is inevitable. A parallel elastic/crystalline viscoplastic FEA code based on a crystallographic homogenization method has been developed using PC cluster. The homogenization scheme is introduced to compute macro-continuum plastic deformations and material properties by considering a polycrystal texture. Since the dynamic explicit method is applied to this method, the analysis using micro crystal structures computes the homogenized stresses in parallel based on domain partitioning of macro-continuum without solving simultaneous linear equations. The micro-structure is defined by the Scanning Electronmore » Microscope (SEM) and the Electron Back Scan Diffraction (EBSD) measurement based crystal orientations. In order to improve parallel performance of elastoplasticity analysis, which dynamically and partially increases computational costs during the analysis, a dynamic workload balancing technique is introduced to the parallel analysis. The technique, which is an automatic task distribution method, is realized by adaptation of subdomain size for macro-continuum to maintain the computational load balancing among cluster nodes. The analysis code is applied to estimate the polycrystalline sheet metal formability.« less
  • In this work, a physics-based thermal creep model is developed based on the understanding of the microstructure in Fe-Cr alloys. This model is associated with a transition state theory based framework that considers the distribution of internal stresses at sub-material point level. The thermally activated dislocation glide and climb mechanisms are coupled in the obstacle-bypass processes for both dislocation and precipitate-type barriers. A kinetic law is proposed to track the dislocation densities evolution in the subgrain interior and in the cell wall. The predicted results show that this model, embedded in the visco-plastic self-consistent (VPSC) framework, captures well the creepmore » behaviors for primary and steady-state stages under various loading conditions. We also discuss the roles of the mechanisms involved.« less